Foundations of a DPLL-Based Solver for Fuzzy Answer Set Programs

摘要

Recent years have witnessed the effort to extend answer set programming (ASP) with properties of fuzzy logic. The result of this combination is fuzzy answer set programming (FASP), a powerful framework for knowledge representation and non-monotonic reasoning with graded levels of truth. The various results in solving FASP make use of transformations into fuzzy satisfiability (SAT) problems, optimization programs, satisfiability modulo theories (SMT), or classical ASP, each of which comes with limitations or scaling problems. Moreover, most of the research revolves around Godel and Lukasiewicz semantics. The former approach is elegant in its attempt to generalize well-known methods in classical ASP to the fuzzy case. In our work we seek to extend this approach under the product semantics, utilizing the fuzzy generalization of the DPLL algorithm. As such, we design the inner works of a DPLL-based fuzzy SAT solver for propositional product logic, which should provide foundations for the technical implementation of the solver.